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Segre-variety RM-type code[1]

Description

Evaluation code of multihomogeneous polynomials evaluated on points of a Segre variety, i.e., on the Segre embedding of a product of projective spaces. These codes are Reed-Muller-type analogues adapted to product projective geometries [1].

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Additive \(q\)-ary codeECC
Linear \(q\)-ary codeECC
Evaluation codeAG ECC
Polynomial evaluation code
Parents
Polynomial evaluation code
Segre-variety RM-type codes are polynomial evaluation codes with \(\cal X\) being a Segre variety.
Segre-variety RM-type code

References

[1]
M. González-Sarabia, C. Renterı́a, and H. Tapia-Recillas, “Reed-Muller-Type Codes Over the Segre Variety”, Finite Fields and Their Applications 8, 511 (2002) DOI
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Zoo Code ID: serge

Cite as:
“Segre-variety RM-type code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/serge, arXiv:2606.11484
BibTeX:
@incollection{eczoo_serge,
title={Segre-variety RM-type code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/serge}
}
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Permanent link:
https://errorcorrectionzoo.org/c/serge

Cite as:

“Segre-variety RM-type code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/serge, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/ag/varieties/segre.yml.